Lipkin



March 6, 1951 c. LlPKlN 2,544,339

AID FOR CARRYING OUT MULTIPLICATION Original Filed Jan. 19, 1946 3 Sheets-Sheet l a4 3 34 as A i i 40% I 37 36 L3 I J '1 2% as 40 INVENTOR. CHARLES LIPKm March 6, 1951 c. LIPKIN AID FOR CARRYING OUT MULTIPLICATION 3 Sheets-Sheet 2 Original Filed Jan. 19, 1946 v W 5 o l N n WWW; W H a 5 MG m :{I Q

M M uni INVENTOR CHARLES LIPKm 3 Sheets-Sheet 3 CHARLES LIPKm March 6, 1951 c. LlPKlN AID FOR CARRYING OUT MULTIPLICATION Original Filed Jan. 19, 1946 fig. 25.

Patented Mar. 6, 1951 UNITED STATES PATENT OFFICE 2,544,389 AID R QA RY N OUT M LT LIQATIQN Charles Lipkin, New York, N. Y. S i u ed for aband a l cation S r al No, 642,199, J anuary 19, 19,46. This application De m 3 .9 8 Serial No, 63, 35

2 Claims.

The present ven io la s to new a d neoful improvements in a device for assisting in multiplication of two numbers and this application is a substitute for my abandoned application Serial No. 642,199 filed January 19, 1946.

More particularly, the present invention relates to an aid for carrying out multiplication of simple and novel construction and operation using the principle of slide multiplication whereby any number or figure may be quickly multiplied by any other number or figure and the product quickly and accurately obtained.

The invention proposes a device embodying two sections slidably joined and held together along two abutting longitudinal edges and eaoh provided with a plurality of wheels rotatably mounted in aligned relation and each wheel bearing numerals from 1 through 9 and. (zero) equidistantly spaced apart in circles. The ciroles should be preferably of corresponding size on both or opposite sides of the wheels so that the numerals may be simultaneously exposed and visible at windows or openings through both or opp e Sides of the ec ons; bu sh ul be reversed o a o d in o ole in eombinetione- Eeoh Wheel ha a P p eral ooth fo eeeh meral or digit so that the rotation of each wheel o e teeth at e me i l adv nc t e .no erele one ,at a time. In conjunction with the slidable mounting of the sections one on the other, the wheels may be so related to each other as to greatly facilitate multiplication of two sets of numbers or one by another so that the product may be quickly ascertained and read.

The invention also proposes and embraces novel means to hold each adjacent pair of wheels in a set position with a minimum number of spring catches bearing in. the recesses between adjacent teeth of each wheel. The teeth of the wheels project centrally into recesses along the remote or opposite edges of the sections to protect the wheels against accidental movement or upsetting when the wheels are set to expose the numerals thereof through the windows or open- ;ings. There is one opening for each wheel at each side of the device or two openings in alignmentat opposite sides of each section to line up with the same numerals duplicated on opposite sides of the wheels. W

The invention also proposes novel means for aligning the numerals'or digits of each wheel of one slidable section with the numerals of any wheel of the other slidable section when the sections are slid one relative to the other. Qne section engaging notches in the other section, spaced relation and alignment with each opposed set of windows or openings and the centers and also t e p ed e eral t h o the ree e t re wheels d erm ne Y., Il on fee w en the catches engage in the notches together with 2 mar in s or ine e t a oon leot ne a h eoo lilm oeee set o Windo s one a o e t e the tol edioete i uall thei ve t ca al ment- The nvent n a so Proposes no el i onetru ti n oi t e sections to rotete o y mount th toothed h ls en eetehee; to eli lolv 'oot eot t e t on fo lidin movem nt' on oh other to p e the va iou oumexele a d sir r latio to e t eeo iolle one on t e oth n ro gressive or other relation with respect to the llmfi fia s 9f t e var ous 9 etlJ' -o n Whittle his el op at n o mu l -ins p cee n a sim le, quick an effieient ma n he e y various nol l r numbe s o gu e ma be multiplied by o e another wit i e mi mu of ti end i filll f' IQ PP 1 o u o tained with e eo sleteele e ille of ime and l bor- :T e invent n a o Pro ose a m t ply n eice of the .e isle t oe x pt that onl t sect ons are emplo ed hese two sections, have two ed es e da ol connected instead of emp yv ing a medial, runner or slip-stick slidable in a groove in the center of an outer rule which surrounds the runner at the back, top and bottom. The numerals or combinations of numbers can be large enough to be easily read without depending upon the slides coming to rest at minute graduations of an engine-ruled scale which is subject to error from"w arping, distortion or in-.- accurate reading as those familiar with such devices will readily appreciate. Because ot the present construction and arrangement, accurate readings can be made even before the slides come to rest at any setting. The arrangement permits mental computation of the product or products of each set of two numbers, which happen to approximate vertical juxtaposition, without even b n in t e sl des to rest ometh n practically mposs le he u e o o o diner ic rule, and with an action which may be said to be almost continuous in its operation or without requiring an appreciable or noticeable pause in ts .eotion in u e This invention also proposes a variation of the numbe of hee s and o enin i t e S ti which are slidably connnected along adjacent longi udi al etleee as no to h aeoid tany d spl or .cli oonneoted t ansv rse y wh n s ated o ul edewe i on; eeebo l e The wheels and openings are so related that the equidistantly e o d w ndows an n mer isib o'el ma be .ete oe a one or d nce n y o de o al nment and th eot o m be extended in either direction the full lengths of the longitudinal rows of numerals on the le- T e h les th ou h whi h t are v si Permit b ie .inetr ot oo fo th o e tion a use of the device to be marked ,on the oppositefaces of the sections to facilitate such use and computings in multiplying by turning the device from left to right or vice versa lengthwise thereas distinguished from tumbling, rolling or turning over from top to bottom or vice versa.

The invention also embraces making the instrument in different ways and of different materials, including the mounting of the wheels, the slidable connection between contiguous edges of the sections with or without the wheels and windows with the numerals thereon, or with the numerals of the numbers to be multiplied together to be written on the slides in proper order and relation and later erased for repeated use of the spaces therefor, care being taken to reverse one of the multipliers, either the multiplicand or multiplier, in order to proceed with the multiplication. It is also preferable to have vertical lines connecting each set of windows and numerals appearing therethrough as they come into vertical position one over the other. Unlike ordinary slide rules, these lines do not have to be exactly in position or accurately aligned as long as they are closely adjacent. The slides or sections need not come to a full stop in order for the user to see which numerals are to be used next in the multiplication and therefore slight warping or misalignment does not interfere with or make any difference in the accurate readings and use of the instrument as would occur in the caseof an ordinary slide rule. No cursor, finder or magnifying glass is needed to show which numerals are to be read in connection with their opposing numerals vertically as with a slide rule where the markings or graduations and numerals are extremely minute and close together as with an engine-ruled scale. With the present device, the numerals are sufficiently large and Widely spaced apart as to be readily discernible, thereby facilitating computations as compared to the use of a slide rule.

For further comprehension of the invention, and of the objects and advantages thereof, reference will be had to the following description and accompanying drawings, and to the appended claims in which the various novel features of the invention are more particularly set forth.

In the accompanying drawings forming a material part of this disclosure:

Fig. 1 is a front elevational view of theinultiplying device or-instrument constructedin accordance with the present invention.

Fig. 2 is a rear elevational view of Fig. 1.

Fig. 3 is an elevational view similar to Fig. 1, showing a different position of the parts and with one end of the instrument partly broken away.

Fig. 4 is an enlarged end elevational view looking from right side of Fig. 3.

Fig. 5 is an enlarged transverse cross-sectional view taken on the line 55 of Fig. 3.

Fig. 6 is an enlarged detailed view of a portion of Fig. 5.

Fig. 7 is an inside elevational view of the front plate of the upper section of the device.

Fig. 8 is a sectional View taken on the line 88 of Fig. 7.

Fig. 9 is a view similar to Fig. 5 of the front plate of the bottom section of the slide.

Fig. 10 is a sectional view taken on the line IB| of Fig. 9.

Fig. 11 is an inside elevational view of the rear plate of the bottom section of the slide.

Fig. 12 is a sectional view taken on the line l2--l2 of Fig. 11.

Fig. 13 is a view similar to Fig.- 11 of the rear plate of the top section of the slide.

Fig. 14 is a section taken on the line |4H of Fig. 13.

Fig. 15 is a perspective view of one of the wheels, per se.

Fig. 16 is a perspective view of one of the latch springs, per se.

Fig. 17 is a view similar to Fig. 3, but illustrating the device constructed in accordance with a modification of the present invention.

Fig. 18 is a rear elevational view of Fig. 17.

Fig. 19 is an enlarged detailed view of a portion of Fig. 17 with parts thereof broken away to reveal interior construction.

Fig. 20 is a transverse cross sectional view taken on the line 20-20 of Fig. 19.

Generally and broadly, the device or instrument of the present invention embodies two sections or slides, slidably connected or associated along contiguous or abutting longitudinal edges so as to slide one relative to the other lengthwise in either direction so that either section may be slid to project at either end with respect to the other section. The sections are held from dis placement edgewise or transversely, that is pulling apart in the plane thereof. Each section is provided with wheels bearing numerals at equidistantly spaced points from 1 to 9 and 0 (zero) on one and/or both sides and means for aligning the same simultaneously when the sections are together, or some of them in different positions, when the sections are slid or extended relative to each other. One section can be projected at one end and the other section at the other end and can he stepped along at uniform spaced intervals to align different numerals in units, tens, hundreds, thousands, etc., columns for alternately multiplying and sliding to facilitate multiplication of various odd or large numbers quickly and accurately. The numerals may be preferably arranged to be viewed on both sides and to expose the same numerals on onposite sides in the same individual positions, but reversed on opposite sides, so that a series of numerals comprising a number are arranged in reverse order as they appear at the inside instead of in the order in which they would appear if written in multiplying so that the operation may be carried on by the device, placing the digits in the proper columns, according to their value and order of use as a multiplier.

- Both or either the multiplicand or the multiplier may be used as a multiplier, and the numerals may appear equidistantly spaced permanently printed, etched or embossed on wheels in circles concentric to a common center of rotation, provided with means such as a knob, pins or teeth positioned on the periphery or radially in line with the numerals to advance the same successively and progressively from 1 to 9 and 0 (zero). The numerals are held in set position according to the numbers or figures to be multiplied one by the other. Means are also provided to hold the sections in set positions throughout their lengths or distance of movement with some or all of the numerals in alignment as described. Means is also provided to hold each wheel in set position.

As shown in Figs. 1 to 16 inclusive, the multiplying device 20 comprises an upper section 2| and a lower section 22. The sections 2| and 22 The upper se'ction2l comprises plates 24 and 25, and the lower section 22 comprises plates 24- and 25 of suitable material, preferably rigid, such as metal, plastic, etc., joined together in any suitable fashion, such as cementing along: edge flanges 26 and 21 and interfitting with each other to provide spaces between the plates bounded by the flanges. The sliding connection- 23 comprises a groove 28' in the lower section 22. and a. rib 29 on the upper section 2|, see Figs. 4 to 6, which have a locking interfit and may be dove-tailedto permit the sections 2| and 22' to slide endwise one into the other, at such connection, at-either end, and to be similarly disconnectedwhile retained against transverse or lateral displacement. In each hollow, center space of the sections 2| and 22 there are wheels 30 rotatably mounted on circular shafts 3| integrally formed on the rear plates 25 and 25 of the sections 2 I and 22. Recesses 32 are formed inthe free ends ofthe shafts 3| and. receive projections 33 integrally on the inner faces of the front plates 24 and 24. The wheels 30 each have ten. teeth 34 equidistantly spaced apart to extend openings 35 equidistantly formed in. the top and bottom. edges of. the sections 2| and 22 to permitstepped rotation of the wheels and. to: protect the wheels against being accidentally turned.

Each wheel 30 also bears numerals 36 from to 9 and 0 (zero), see Figs. 3 and 15, on opposite sides radially aligned with the teeth to be advanced or stepped along therewith progressively. The numerals 36 arepositioned to appear simultaneously' through. aligned; windows 3.1. formed. in; the: plates of both sections. 2| and 22;. Thenumerals on opposite faces of. the. wheels, 30 are transposed or reversedlso' that the same numeral. will appear in the aligned windows-.31. of: sections in. any, givenv rotative positions; of. the. wheels 30.. Means: are provided forv holding, therwheelss 3| in desired adjusted rotative positions in which the desired numerals 36 will be aligned with the windows 31. The means comprises leaf springs 38 preferably constructed of spring steel or other similar flexible material. The springs 38, between each pair of wheels 30 have their ends secured. in suitable aligned lugsv 39 formed onzthe inside faces of the platesof eachof the sections-.-v The. springs 38' have their ends securely attached to. one of theirv supporting lugs. 39 by means of glue or any other suitable securing means, to retain the springs 38 in position. The freeends of the springs 38 are bent into somewhat fiat'-= tened V-shapes. to'seat in the notches between. adjacent teeth 34 of the wheels, as shown. in. Fig. 3, to retainthe wheels 30 against accidental rotation. When the wheels 30 are manually turned in one direction or the other, the free ends of the springs 38 will? merelysnap from one notch to the next.

Inusing the. device of the: present invention, the sections 2| and- 22 are to-be slidlongitudinall'yrelative. to one another" to vertically align the. windows. 31 to. permit. the; numerals: in veri tically aligned windows to be" multiplied mentally, as: will. become clear as; this: specification proceeds... The: opposed faces: of the sections: 2| and. 22: on oppositeasides of the meeting edges 23 of the sectionsv are formed. with short vertical lines 40 whichv extend from thewindows 31' to the meetin'g'edges 23', seeFigs. lt'o 3-. When thewindows' 31 are in vertical alignment, the lines 40: will be in end' alignment as' shown in Fig; 3.

The* faces of the sections 21 and 2 2 are also provided 'with small-asterisks 4| adj acent opposed" windows 31. These: asterisks M are provided'to be vertically aligned at the start of each multiplying operation to designate the proper starting position of the device. The asterisks 4| are etched, printed, embossed. or in any other manner formed on the opposed faces of the sections 2| and 22.

To retain the sections 2| and 22 against accidental. longitudinal movement during. the course of solving a multiplication problemon the device, the bottom face of the. rib 29 is formed. with a plurality of. equally spaced recesses 42. As shown in Fig- 1?, there is a recess 42' beneath each of. the. windows 31. The base wall of the groove 28- is formed. with a plurality of upstanding rojections 43,. one for each of the recesses 42.. The projections 43 extend. intothe recesses 42 and retain the. sections 2|. and 22 against longitudinal movement. unless the sections" are manually forced' in one direction or the other to cause the projections to snap out of the recesses 42 with which they were engaged and to snap into the recesses in the newly aligned position of the sections 2| and 22. As is apparent from Figs. 6, 9" and 11, the projections 43 are partially formed. on each of the plates 24 and 25 forming the lower section 22' of the device.

The operation of. the: device is as follows;

To? start a multiplication problem, the sections 2| and 22 are first slid' longitudinally to the posi-- tion shown in: Fig. 3, and all of thewheels- 3B are turned to the positions in which. the zero digitswill be visible in the aligned window openings 31..

Let us assume, for the sake of illustration, that it is desired to multiply 291,736 by 261,408. The wheels 30 of the top section 2| are then turned to show the digits of the multiplicand, 291,736, in. the windows 3'! of the top section, as shown inv Fig. 3. The digits of the multiplier, 261,408, are

. then set up in the windows 31" of the lowersection' 22; however, it will be necessary to set upthe' digits of' the multiplier in the reverse order.v This is'done by turning the device over, as shown. in Fig. 2, and then aligningv the digit of the multiplier with the" windows 3! on the back of thelower section 22' in proper order; On the back: side, the digits of the multiplicand, aligned with. the windows 3'! of the top section 2|, appear in. reverse order as shown in Fig. 2.. After all the digits of the multiplier have been set up in the: windows 31 of the bottom section 22, the deviceis again turned over to: expose the front face. On the front face, the digits of the multiplicand,v 291,736, will appear inproper. order in the windows 3T of. the top section 2|. and. the digits of the multiplier, 261,408, will appear in reverse order in the windows. 31 of the lower section 22. The sections 2 l' and 22' are then sl'id'longitudinally relative to each. other in a direction to vertically align the asterisks 4i bringing the opposed end-- most digits 6 and 8 into verticalalignment. The digits of the top and bottom sections will then appear this way:

multiplying together the superimposed digits. 8 6=48 and then putting down the 8 on a sheet of paperandcarrying the 4.

' The sections 2 and 22' are then slid to vertica'll'y align the two' digits at the adjacent ends Then the vertically aligned digits are multiplied together and their products are added together and the sum of those two numbers is added to the 4 carried over from the previous multiplication; 8 3=24 6 0=0 24 plus plus 4 equals 28. The 8 i then put down on the sheet of paper to the left of the eight of the previous multiplication; thusly, 88, and carry the 2."

Completion of the multiplication is then carried out by again sliding the sections 2| and 22 to vertically align the three digits at the adjacent ends of the numbers, so that they appear this way:

Then multiply the vertically aligned digits and add the products; 56 plus 0 plus 24 plus the 2 carried from the previous multiplication equals 82. Put down the 2 (288) and carry the 8.

Again slide the sections 2| and 22 to vertically align the four digits at the adjacent ends of the numbers, so that they appear this way:

Then multiply the vertically aligned digits and add their products; 8 plus 0 plus 12 plus 6 plus the 8 carried from the previous multiplication equals 34. Put down the 4 (4288) and carry The sections 2| and 22 are again slid longitudinally to vertically align the five digits at the adjacent ends of the numbers, so that they appear this way:

The vertically aligned digits are multiplied and the products are added; 72 plus 0 plus 28 plus 3 plus 36 plus the 3 carried from the previous multiplication equals 142. Put down the 2 (24288) and carry the 14. i

The sections 2| and 22 are again slid to vertically align the six digits of the two numbers, so that they appear this way:

opposite ends of the lines of digits, so that they appear this way:

Multiplication and addition are again carried out 0 plus 36 plus 1 plus 42 plus 6 plus the '7 carried from the previou multiplication equals 92. Put down the 2 (2124288) and carry the 9.

Again slide the sections 2| and 22 to vertically align the four digits at the adjacent ends of the numbers, so that they appear this way:

Multiply the four vertically aligned sets of digits and add their products; 8 plus 9 plus 6 plus 14 plus the 9 carried from the previous multiplica tion equals 46. Put down the 6 (62124288) and carry the 4.

The sections are then slid longitudinally to vertically align the three digits at'the adjacent ends of the numbers, so that they appear this way:

Multipl the three vertically aligned sets of digits and add their products: 2 plus 54 plus 2 plus the 4 carried from the previous multiplication equals 62. Put down the 2 (262124288) and carry the 6.

The sections are then slid longitudinally to vertically align the two digits at the adjacent ends of the numbers, so that they appear this way:

Multiply the two vertically aligned digits; 4 plus the 3 carried from the previous multiplication equals '7. Put down the "7 (76262124288). Thus, the product of multiplying 291,736 by 261,- 408 is 76,262,124,288.

It is apparent from the foregoing that a simple device has been provided to facilitate the multiplication of any two numbers having not more than six digits in each number being multiplied. It is possible to multiply numbers having more than six digits in one or both numbers, but then the device will have to have more than six wheels 30 in each of the sections. The multiplication can also be carried out by using the back side of the device, but then the digits of the multi 9 plicand, 291,736, will appear in reverse order and the digits of the multiplier, 261,408, will appear in proper order.

In the modification of the invention shown in Figs. 1'7 to 20, inclusive, the structure is somewhat similar to that previously described. The top and bottom edges of the sections 2| and 22" are closed and smooth as indicated at 45 and the edges of the wheels 30' are smooth. However, the front plate 24 of the upper section 2| and the rear plate 25 of the lower section 22' are provided with circular slots 46 of nearly 360 degrees and the wheels 30' are provided with equidistantly spaced holes 41 aligned radially with the numerals 36 and aligned with the slots 46 so that a pointed object may be passed through one of the slots 46 and into one of the aligned holes 41 for turning the wheels 30. This manipulation exposes the desired numerals 35 through the windows 31' to expose the required digits of the numbers to be multiplied together in the same manner as before described.

A resetting device is provided for the wheels 30, to set them all simultaneously back to (zero). This resetting device consists of a pinion 48 fixed on each wheel 30', a shown in Figs. 18 and 19, and a rack 49 slidable between the plates of each of the sections and having spaced sets of teeth 50 to engage the pinions 49 and turn the wheels 30 back to their starting position.

Normally, the spaces between the sets of teeth 50 of the racks 49 are aligned with the pinions 48, so that the Wheels 30' are free to be manually rotated independently of each other to align the desired numeral 38' with the respective window openings 31'. Also, the pinions 48 are formed on one side, in radial alignment with the numeral 5, with a toothless area 48, see Fig. 19. The racks 45 have similar toothless areas 49' which cooperate with the toothless areas 48' of the gears in the fully in positions of the racks, to free the wheels 30' from the racks 49 when the wheels have been turned back to their positions in which the numerals 0 are aligned with the window openings. Opposite ends 49 of the racks 49 extend from opposite ends of the device to be pulled outward for turning the wheels 3|) back to their position in which the zeros will be aligned with the window opening 31'. Upon being pulled out the spaced teeth 50 of the respective racks 49 immediately mesh with the pinions 48 and turn the same until the zeros are aligned with the window openings 31' and the toothless areas 48' of the pinions 48 become aligned with the spaced teeth 50 of the racks 49. Rotation of the wheels 30 then stops and after the racks 49 have been completely pulled out they are immediately returned to their starting position with no effect on the position of the wheels 30' as the toothless areas 48' of the pinions 48 will now be facing the spaced teeth 50 of the racks 49. The return movements of the racks 49 again align the toothless areas 49' of the racks with the toothless areas 48' of the pinions 48 leaving the wheels 30 free to be manually rotated independently of the racks 49.

When free of the spaced teeth 50 of the racks 49, the wheels 30' are held against rotation by means of leaf springs which have their intermediate portions secured in position between spaced lugs 52 formed on the plates of the sections 2| and 22. The ends of the springs 5| are bent to engage complementary notches 53, see the bottom portion of Fig. 19, formed in the periphery of the wheels 30'. When the wheels 10 30' are turned, the ends of the springs 5| merely nap into and. out of the notches 53. The notches 53 are formed in the periphery of the wheels 30 in, radial alignment with the numerals 36.

In other respects this form of the invention is similar to the previous form, and like parts are identified by the same reference numeral with a prime added.

While I have illustrated and described the preferred embodiments of my invention, it is to be understood that I do not limit myself to the precise constructions herein disclosed and the right is reserved to all changes and modifications coming within the scope of the invention as defined in the appended claims.

Having thus described my invention, what I claim as new, and desire to secure by United States Letters Patent is:

1. In an instrument of the class described having a pair of like adjacent hollow sections formed with aligned window openings and enclosing rotatively mounted discs carrying numbers to be multiplied which can be selectively exposed in the window openings, a rib formed on the edge of one of the sections facing the other section, the other section having a groove formed in its adj acent edge portion into which said rib is slidably engaged, said groove opening to the ends of its respective section leaving the sections free to be slid relative to each other with their ends projected beyond each other in either direction to align the numbers, and means releasably retaining the sections against sliding movements with desired numbers aligned.

2. In an instrument of the class described having a pair of like adjacent hollow sections formed with aligned window openings and enclosing rotatively mounted discs carrying numbers to be multiplied which can be selectively exposed in the window openings, a rib formed on the edge of one of the sections facing the other section, the other section having a groove formed in its adjacent edge portion into which said rib is slidably engaged, said groove opening to the ends of its respective section leaving the sections free to he slid relative to each other with their ends projected beyond each other in either direction to align the numbers, and means releasably retaining the sections against sliding movements with desired numbers aligned, said retaining means comprising upstanding projections formed on the section formed with said groove, said projections being located within said groove one in lateral alignment with each of the windows, and corresponding grooves formed on said rib and engaged by said ribs.

CHARLES LIPKIN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 460,930 Cox Oct. 6, 1891 508.435 Miller Nov. '14, 1893 779,088 Locke Jan. 3, 1905 1,165,058 Behan Dec. 21, 1915 1,764,915 Vethe June 17, 1930 1,961,053 Kubler May 29, 1934 2,380,846 Josepho July 31, 1945 FOREIGN PATENTS Number Country Date 7,819 Great Britain 1902 101,705 Great Britain Sept. 24, 191'! 

